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A number of bullets are fired horizontal...

A number of bullets are fired horizontally with different velocities from the top of a tower they reach the ground

A

at same time with same velocity

B

at different times with different velocities

C

at same time with different velocities

D

at different times with same velocity

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the motion of the bullets fired horizontally from the top of a tower. ### Step-by-Step Solution: 1. **Understanding the Scenario**: - Bullets are fired horizontally from the same height (the top of the tower). - The initial vertical velocity of the bullets is zero since they are fired horizontally. 2. **Vertical Motion Analysis**: - The time taken for an object to fall freely under the influence of gravity is independent of its horizontal motion. - The vertical motion can be described by the equation of motion under gravity: \[ h = \frac{1}{2} g t^2 \] where \( h \) is the height of the tower, \( g \) is the acceleration due to gravity, and \( t \) is the time taken to reach the ground. 3. **Time of Flight**: - Since all bullets are fired from the same height \( h \) and are subject to the same gravitational acceleration \( g \), the time \( t \) taken for all bullets to reach the ground will be the same, regardless of their horizontal velocities. 4. **Horizontal Motion Analysis**: - The horizontal distance traveled by each bullet will depend on its horizontal velocity \( v \): \[ d = v \cdot t \] - Different bullets will have different horizontal velocities, thus they will cover different horizontal distances while falling. 5. **Conclusion**: - All bullets will reach the ground at the same time but will have different horizontal velocities and travel different horizontal distances. - Therefore, the correct statement is: "at the same time with different velocities." ### Final Answer: The bullets reach the ground at the same time with different velocities. ---
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